The Byzantine Dice of Torg

I played in a session of the new edition of Torg last night (well, a few nights ago now, but it was last night when I wrote the first 2000 words that follow). It was fun, but, man, are the die rolls complicated and weird in this RPG. I'm really glad we were playing over Roll20, because I wouldn't want to try to engage with the core mechanic of Torg without die-rolling software.

To use a skill in Torg, you: Start with your Attribute value, add your skill value,  and add any miscellaneous modifiers (like +4 for an All-Out Attack that leaves you Very Vulnerable afterwards).

So far, so good, it's not sounding any more complicated than d20 games.

Now you roll a d20, but instead of adding your roll to the total above, instead you look at a chart that converts your 1d20 roll into a Bonus from -10 to +7.
 

Okay, that's a little weird. Not horrible, but already a tiny bit clunky and hard to intuit what your average roll will actually be. At first, I thought the chart was flattening the roll by making the average roll more common... but on studying the math of the chart, I quickly realized it doesn't do that at all.

Things are going to get a whole lot stranger from here on out.

If your die roll was a 10 or a 20, it "explodes", giving you another die to roll, which can also explode if it rolls a 10 or 20. So it's a system with the potential for arbitrarily large successes, big memorable die rolls where you out-perform anyone's expectations. This is technically infinitely open-ended, but the progression of the resulting modifier slows down once you go further up the chart than a 20. So while a natural roll of 20 is +7 bonus, a total of 50 (which requires exploding at least twice to accomplish) is just +13.

Except, you can't actually roll a 20, because the natural 20 would explode, as would any roll of 50 (20+20+10 explodes for a 4th die, for example). So as near as I can tell, the entry for the +7 result (which only happens on a 20) is almost never needed, and the entry for the +13 result actually happens on 46-49, not 46-50 as the chart indicates. For that matter, the chart says a of 9 or 10 roll is a -1 bonus, but you can't normally actually roll the 10, so that's also somewhat misleading.  Well, you can roll a 20, 30, 50, etc, but only if you've got a bonus die from an Ups or Possibility (both of which are described below). Rolling an exact 10 is even harder to do (and requires an Ups).

So what is the actual average roll? The math is kind of tricky, but I made a big spreadsheet to figure it out.  The average rolled bonus is... -0.26127955.  Yep, on average, you'll roll slightly less than your Attribute+Skill combination. Which is counter-intuitive, because the potential for big memorable high-value rolls makes you expect that you ought to be averaging rather higher than your stats. That is not the case at all.

An aside about approximations: I only calculated rolls of 80 or less, so I'm probably low-balling it by a few one-thousandths of a percent. Rolling above an 80 requires rolling a "20" four times in a row, or a "10" eight times in a row, or some combination splitting the difference like 10-20-10-10-20-10. The odds of scoring above an 80 are less than 1 in 10,000, so I figure it's probably safe to round off at that point. Calculating it only to rolls of 70 or less returned an average of -0.26271358, a variation of only one one-thousandth of a point of bonus, and I'm pretty sure the math runs out to diminishing returns even as you approach infinity.

Yes, you could technically roll a one-million Bonus, but if you ever did the game would grind to a halt of multi-hour die-rolls and a re-enactment straight out of Rosencrantz And Guildenstern Are Dead. I'm not going to hold my breath waiting for that to happen, and I don't feel I need to extrapolate the math out that far, either, just for the sake of accuracy.

So at that point, I'm already really glad that Roll20 has a die-rolling function that calculates it all in the blink of an eye. In our session, we had two rolls that were above 60. While rolling a d20 three to five times and counting up the math out loud would have been dramatic and awesome, it's also likely to feel weirdly clunky, and kinda suspicious. Like, if the same person rolled a 61+ twice in the same session, as GM I'd start wanting a closer look at his dice. Maybe I'm just an untrusting jerk, though. Roll20 eliminates the chance of dice-deception, so I didn't have to worry about it.

So the next question that springs to mind is how often you succeed at the standard difficulty. For that we need to know a bit about Character Creation. Characters are made with a point-buy method, and your point budget matches an average Attribute of 8. You're given 16 skill points to spend, with an initial cap of 3 in any skill. In my limited experience from making a single character, it seems like there are more than 8 skills that you'll want on any given character (I ended up putting points in 10 skills for my fairly simple fighter-y Edeinos character, because it would have taken 13 different skills to represent the more ranger-y concept I'd wanted), so you're almost certainly going to have a 2 or less in any skill that's not the centerpiece of your character. 8+2=10, and the Standard Difficulty listed as default is a 10, and the average roll reduces your Total, so you can expect to have a less than 50% chance to succeed at a random task. You will, of course, likely focus your character, getting an 11 or so in your best attribute, brought up to a 14 by the skill bonus. This comes at the cost of most likely having a 6 on some attribute (4 out of 5 PCs last night had a 6 in Charisma, and my character had two 6s and a 7 to afford his 10 Dex and 11 Str), so there are definitely going to be critical rolls that face a very low chance of success, and those will pop up from time to time regardless of your efforts to avoid them (unless you give your PC an 8 in all 5 stats and spread your skill points thin, too). Succeeding at an average Difficulty with a 6 attribute and no skill requires rolling a 17 or higher (or an exploding 10 followed by a 7 or higher) on the die, which works a 23.5% chance of success.

That is assuming that Difficulty 10 is the norm. While it is the stated Standard Difficulty, there's plenty of reason to expect that the actual Difficulty you're shooting at is going to vary from that quite often. Instead of a single Armor Class and maybe a few kinds of Saving Throw, each character has about 10 different defensive values calculated from their other stats, and the potential to take an Active Defense Action to raise the difficulty from an attack.

But it gets even weirder and more elaborate from there, as Torg has degrees of success, so it's not just hit or miss, succeed or fail. It's failure vs standard success vs good success vs outstanding success, with increasing degrees of success adding on extra beneficial results. Contrast this with D&D. In D&D, once I know the enemy's AC is 15, if I roll high I don't have to do any math and can skip straight to damage. In Torg, even if I know the enemy Melee Defense is 12, and I just rolled a 18, I still have to look at the chart, find that 18 = +5 bonus, add that to my 10 Dexterity and 3 Unarmed skill to know my total post-bonus is 18, then subtract his Defense of 12 to get 6 and know that I have a Good-ranked hit, which will do bonus damage. Again, with Roll20's lovely die-roller and the output from the automated character sheets this is pretty painless, but I imagine all that math would murder the pacing of a face-to-face game.

Torg also gives you a lot of ways to reroll or add a die, and all of those rerolls have special rules of their own. Before we can discuss these rerolls, however, we need to explore the Mishap rule, which can shut down your rerolls completely. Certain types of Actions are prone to Mishaps. These are generally high-risk Actions like full-auto gunfire, and spellcasting. These Actions will trigger a Mishap if the first die rolled is a "1", and some Actions may have a higher Mishap range (up to a 4 on the die in some cases). Mishaps are automatic failures (regardless of stats) that can't be rerolled, and they usually also trigger some sort of critical fumble consequence. None of my Actions were Mishap-applicable last night, but I was involved in a shooting-into-a-Melee situation, which we will discuss later, because it interacts very strangely with some of the reroll options.

One of the reroll options my character had available was that I was able to make "Favored" rolls in melee and stealth. During character creation, I read this sort of like having Advantage in D&D, but I was very wrong, as functionally it's quite different and not nearly as strong. Favored is a re-roll, rather than rolling twice and taking the better result. Since more than half the rolls in Torg have a negative "Bonus" (and the average Bonus is negative as well), Favored rolls are somewhat unlikely to produce a good result. Let's say I roll a 13, for a meager Bonus of +1. If I invoke my Favored ability, I will improve my total only 34% of the time. I will break even 10.5%, and I have a 55.5% chance of actually hurting my results. So invoking my Favored reroll is usually a poor choice in that situation.

So it seems like Favored is mostly useful to prevent really bad results, but you'll recall that a Mishap cannot be re-rolled, so for some types of die rolls, Favored doesn't actually mitigate the worst results, either. Which more or less means that Favored is only useful if the GM is very transparent about the Difficulty Numbers. Thankfully, page 260 of the Torg Eternity rules specify that the GM should be very forthcoming with difficulties. I didn't realize that last night, and as a result I felt like my Favored abilities were actually pretty useless. After all, I'm only willing to risk using Favored to reroll a +1 roll if I'm pretty certain that the +1 is a failure.

Having read the rulebook since last night, I now know that I can actually quiz the GM about the monster's stats. That seems weird to me, as it is very gamist and spoils some of the mystery that most RPGs provide by default. That said, I spent both of the two Perks you get in character creation to buy Favored status on die rolls, so if I don't want to feel like I wasted my choices, I'm going to have to invoke page 260 a lot (even if it does feel a little weird to me to do so). Honestly, having such non-intuitive math at the core of the game probably means you do have to be forthcoming with mechanics and target numbers if you want the players to ever be able to make the intelligent decisions that skilled characters should be making in-universe. The math is so fiddly, you can't really be sure your gut instincts are going to be probabilistically accurate.

Let's move on to the next type of reroll: The Up. Ups are really more of a bonus die than a reroll. They are triggered by certain cards, and generally affect the entire party of Heroes for a round.

Yep, eagle-eyed viewer, you read that right. We are 1,800 words into a discussion of the complicated mechanics of Torg Eternity, and I am just now making my first mention of any of the three major card-based mechanics in the system. Man, this game is weird.

Ups add a second die to every roll. These are combined into a single die roll value, but the rules say the second die is added after the first roll, probably to preserve the chance of a Mishap. Either or both dice may explode. So what do Ups do to the success rate? That math makes my previous calculations look like child's play. After a lot of number crunching, I think it works out to the average roll with an Ups being about +6.185. The doubled opportunity for exploding dice really gives it a shot in the arm, pushing it above the value of simply being double the roll. Going from -0.26 to +6.2 is a very strong swing in the PCs favor.

Again, I didn't take the math out terribly far (nothing above a roll of a 63 in this case, but it still took a hell of a lot more number-crunching to get that far than it did to get to 80 on a normal roll), so if anything I'm possibly underestimating the results by possibly as much as a few one-hundredths of a point.

Ups are rare, but I don't have ready access to the cards that trigger them, so I'm not sure how rare. When they kick in they often (maybe always?) affect the rolls of the entire side. So GMs need to be aware that when the card comes up that gives the PCs all Ups, they will crush the opposition mightily that round, and it may end your fight scene (and your major villain) earlier than expected.

The rules implied this Ups only appears on cards that help the Heroes, but I don't have the cards in front of me to be certain of that.  In the unlikely event that a card exists that gives Ups to all NPCs, the GM would likewise need to be prepared for the TPK that would likely cause. That threat of a TPK makes me suspect that bad-guy across-the-board Ups cards probably don't exist. For the most part, the cards exist to make the PCs look like badasses, not to randomly end your campaign anti-climactically. Or at least, that's the impression I get from the percentage of the cards that I have seen after 1 session of play.

The final, and probably most common, form of reroll is spending Possibilities. These are like Bennies in Savage Worlds or like Drama Dice in 7th Sea. You spend one to roll an extra die and add it to your total, and what's more, if the extra die rolls less than a 10, you get to count it as a 10. So in that way, it's even better than an Ups. The thing about the minimum value of a 10 is kind of crazy in that it is super good if your original roll was pretty awful, and only provides a very modest bump if your original roll was strong. It's a weird system, but kind of beautiful.

Let's say you have a combined attribute plus skill of 12. You rolled a 2 on your first die, resulting in a -8 "Bonus", so your final Action Total is a 4, which is almost always going to fail at anything. You spend a Possibility and roll poorly, so you get the minimum bump of turning your 2 into a 12. The Bonus on a 12 is +0, bringing your final Action Total up to a 12, so you've gone from a guaranteed failure to what is very likely a success.

Now let's say the same character rolls a 19 on your first die instead, resulting in a +6 Bonus, for a final Action Total of 18. You spend a Possibility and roll poorly, so you get the minimum bump of turning your 19 into a 29. The Bonus on a 29 is +8, so your final Action Total is 20. It's only an effective increase of +2 to your total, which might not even be enough to change the degree of success. 
 
There is definitely something really cool about how all the math works out on that. It's kind of awesome... but it's also just really arcane and complicated. I can admire how tightly and precise this system runs, and yet be really glad I'm not having to calculate it all by hand on the fly while people at the table are waiting for their turn. Once again, Roll20 makes an otherwise unwieldy mechanic very playable.

So now that I've explained all those different re-roll and added-die mechanics, I'm going to pivot and talk about a related rule in the game that really doesn't seem to fit well at all with everything else the game is doing. As described above, you have a mechanical base where rolls are open-ended, with varying degrees of success and lots of tools for turning a bad roll into a strong result. The game shines a spotlight on players, sometimes going so far as to empower the party to suddenly smash through against hardened enemies and wrap up a battle way early. So how do you imagine that game engine handles shooting into a melee? You might expect that firing into a melee scrum where a fellow PC is wrestling with a bad guy would mean that you had to be wary about the consequences of a Mishap. You'd be wrong. The Mishap rule doesn't apply in that situation. Instead, it's far worse. Seriously, shooting into a melee is damnably nasty in this game. Don't do it!

Whenever you shoot into a melee, if your die roll is odd, you hit a random participant instead of your target. So that right there is a little surprising, because the characters are mostly hypercompetent badasses, so the notion that they would have a close to 50-50 chance to shoot the wrong person by mistake seems odd. Again, the math turns out to be really complicated, because it's not just an equal distribution of odds and evens on a normal d20. You can't roll a 10 or 20, but you could roll a 37, so it's not 50-50 exactly.

In our session, the villain had taken a child hostage. I rushed forward to try to wrest the baby from their grasp, and succeeded, but the movement rules are a little vague (it's not really a map-and-miniatures game, at least not as our GM was running it), so when my action was done I was still arguably engaged with the villain. Another PC went to shoot him. They did a called shot to the head, and rolled an outstanding success... but the die was odd! So this effectively canceled out their success and their called shot, and meant they would instead hit a randomly determined person in the scrum: that being either the villain, or me, or the child. So a 2/3rds chance of disaster! It came up the bad way on the first roll, and the player's instinct was to spend a Possibility to add an extra die to the roll in hopes of making it even. At first glance they assumed it meant a 50-50 chance of fixing the problem. It doesn't however, because any roll less than 10 on the Possibility die is treated as a 10, meaning the overall total was still odd. Effectively, the extra die had 5 sides that would save my bacon and 15 sides that would kill me or the baby! Thanks to some card play, I survived. Obviously I'm not an objective observer, having been in the center of the target zone, but it definitely strikes me as a weird design choice to forgo the existing Mishap mechanic for something that's a lot more punishing.

3,100 words, and I still haven't gotten to the card mechanic. Damn. I guess this will have to just be an article on the dice, because if I dive into the card decks right now, who knows how deep I'll have to go before I can surface.  For now, let's just acknowledge that the cards enhance the game, but they also ramp up the complexity that much further.

TL;DR: Torg Eternity is math-intensive, card-driven, and chart-reliant. Playing on Roll20 with the button-programmed character sheets and custom die rolling API works like a charm, but I don't think I would want to play (or run) the game on the tabletop with nothing but dice and charts. Thankfully, online technology still works in my native Cosm.

On my Crunchometer, this is a big shiny c24. It looks weirder than it actually plays, and at first glance you might misjudge what it actually is. It's definitely not something that I feel every gamer needs in their collection, but I'm happy to have one in my dice bowl, even if it's mostly just to show off and gawk at. It's more complicated than the current edition of D&D.

Diminishing Returns in Savage Worlds

While righting that last post, I realized something that almost was a bullet point, but deserves it's own attention as a separate topic. I've long wondered about exploding d4s.

Not some clandestine CIA plot to eliminate Castro's D&D group, though that could make for an interesting tale, I'm sure. Hmm... there's a one-shot concept in there somewhere.

Instead, by "exploding", I'm referencing dice that you get to reroll and add to the total if they score their highest face. I think Savage Worlds calls it Acing the dice, but I first encountered it in 7th Sea, where it's said they explode. If you rolled a "10" you'd roll again and add 10 to the total. If you rolled a second ten, you'd roll a third time and add 20 to that roll.

Exploding dice have strange interactions with systems that use multiple die types. Barring explosion, the average roll of each standard die type is 1 higher than the die type preceding it (except the jump from d12 to d20, of course), so a d4 roll averages 2.5, a d6 roll averages 3.5, etc. However, that flat progression falls away when you start messing with exploding dice. The average roll of an exploding d4 is about 3.56, and the average roll of an exploding d6 is about 4.19. Those numbers aren't quite accurate - I'd have to take the math out past several more explosions to figure out the actual repeating digits. But, it should be clear from these aproximations, that there's diminishing returns. Each consecutive upgrade in die size gives you a smaller boost to your average roll.

It's worth noting that since dice explode, there's technically no upper limit to rolls. Sure, you're probably not ever going to get "6" two dozen times in a row and score around 150 on a roll. But getting a d4 to roll "13" will happen from time to time, and I've yet to see (only 3 sessions of actual play) a difficulty above 10. If that holds true, then die size doesn't end up mattering much. An exploding d6 has a 1 in 12 chance of hitting difficulty 10, and a d10 only has a 1 in 10 chance. The d10s a little better, but not a lot.
The most common difficult I've experienced as a player is "4". A d4 has a 25% chance of hitting that, a d6 has 50%, a d8 has 62.5% chance, and a d10 has 70%. Again diminshing returns.
All this does for me is reinforce my deep-rooted desire to buy my d4s up to d6s.

So, with diminishing returns, and the possibility (though infrequent) of the lowliest die scoring any number the best die can score, you'd expect the system to make high die-code skills fairly cheap.

Nope. To get a high die-code in a skill, you typically first buy a high rating in the Attribute it's linked to. That costs points from a very limited pool, so some other attribute will "suffer" for it. (Again, having the low die in something ain't that horrible, but Attributes also generate some static numbers that are based on non-exploding averages or maximums, so it can hurt if you chump stat the wrong the Attribute.)

If instead you choose to buy the skill above the corresponding Attribute, then the higher levels cost double. That double cost hardly seems worth it, since you're at the point of diminishing returns. Especially since those same value in points will buy you another Edge. Edges are special powers (like Feats in D&D) - they make your character unique, and they are almost always of greater benefit than just rolling a slightly larger die.

Damnit. Now I've worked myself into a weird place. I've pretty much convinced myself that there's illogical flaws in the Savage Worlds system. However, I have friends playing said system, and I've very much enjoyed meeting them, gaming with them, etc. I'm quite certain I'll continue playing with them. I'm tempted to steer them to Fate (or more Wushu), but doubt they'll make that switch based on my recommendation. After all, I haven't even read the Savage Worlds book, and haven't given it a fair try, and I'm still the new guy of the group. I've done an analysis that tells me that taking a skill above a d8 is dubious, but I see d10 skills on PC sheets at game night quite often. Either there's something I'm missing, or they just haven't analyzed the math. My personal code of conduct won't let me sit quiet on this discovery. Munchkins game the system and keep the secrets to themselves - not me. But you can't put the genie back in the bottle. Clearly, any future PCs I make will be from an informed viewpoint. So I'm going to have to point it out to the group, which will lead to spirited conversation. Natural human reaction is to say "no, I'm not in error" and debate, so they'll want to. Since I've never read the book, I'm inadequately prepared for that debate - there could be balancing factors I'm missing. So that means I have to go buy a book for a game I would not choose to run. I'll be buying it for the express purpose of talking my friends out of running it, and/or figuring out the optimal character builds, should talking them out of it be impossible. That whole situation stinks. I kinda wish I'd never run the math that lead to this conclusion.

(And no, I can't just ask to borrow theirs. We've known each other for a short time, or rather, a small number of events over several months. Long enough that someone might spontaneously offer, but still new enough you'd seem impolite to ask. Besides, if I'm going to turn a whole group off of a company, the least I can do is throw one final sale in that companies direction. Luckily, I think there's a $10 or $12 pocket guide to the game, which will assuage my guilt without hurting my budget.)

Dissapointing Star Trek RPG Dice System

As mentioned in my previous post, I played the Last Unicorn Games' edition of the Star Trek RPG last night, and I had something to say about the game...

The dice mechanic is (in my limited experience) in a word, dumb.

You roll X number of d6's, and use just the highest, then add Y. X is determined by your Attribute + SubAttribute + Advantages. Y is determined by your Skill + Specialization + Advantages.

The only thing shaking this up was that each roll gets one wild die that can explode. But of course, it does so only 1 time in 6 and typically results in a +50% increase when it happens.

My Vulcan Chief Engineer rolled 5d6 for most science or engineering rolls, which almost always meant his best number was a 6. I then had 3's in nearly every tech skill/specialization, so I rolled a very consistent "9" for my final value. Out of probably 15 or 20 rolls for the evening, I had one "7", one "12" and the other 14 to 18 rolls were all "9"s. Since the most common difficulty was 9, and generally no benefit for rolling above the difficulty, it felt like the dice were irrelevant.

It is very unclear to me what they were trying to model. Not even Commander Data was ever that consistent.

I'm not sure I see the value of a system that leaves so little room for variance, yet requires so many layered dice-modifiers to get there - the same thing could have been accomplished by "roll a single d6, and just hope you don't get a 1" or by a far more elegant diceless mechanism of some sort. Why have all the extra bells and whistles if most don't matter at all?

One of my fellow players rolled 5 dice on something and got four 6's (and a 2) which caused him to cheer! However, since his wild die was the lone non-six, it didn't explode. His skill and specialization only added +2, bringing his total to an 8, and he needed a 9 to succeed. Having "the whiff factor" on a roll that elicited an instinctual cheer was really frustrating, and led to us all wondering why we even roll anything but the wild die.

I've got two Star Trek RPG books on my shelf. We've never played, but we like the show (well, some of them) and so held on to the books just in case we ever get a Trek itch. Now I need to look more closely at them. If the core mechanic is such a let-down, it may not be worth keeping the books.

Exploding Dice

Some RPGs have a mechanic called "exploding dice" - in general, it means that if a die rolls it's highest value, you roll it again and add both rolls together. Example: You roll a "6" on a d6 - in a game with exploding dice, you'd roll the 6 again and add both rolls together. In some versions, a second "6" result would mean a third roll and a result greater than 12.

Most people who read this blog are probably familiar with the concept and the term, but I'd rather just explain the reference here rather than have to explain it again every time I mention the term.

One interesting side-effect of exploding dice is that certain results can't be rolled, and your bell curve ends up lop-sided. Using the d6 example above, you can roll 1-5, 7-11, and 13-17, but you can't ever roll a 6, 12, or 18.

This can have major impact if your gaming has a sliding difficulty scale. If the difficulty was 5, and you apply a standard +1 difficulty modifier, you've just cut the chance of success in half (from 33% to 16.6%). However, a second +1 difficulty modifier on the same roll doesn't impact the chance of success at all (stays at 16.6%), and a third +1 difficulty modifier only reduces it slightly (from 16.6% to 13.8%).